Geosci. Model Dev., 7, 2193–2222, 2014 www.geosci-model-dev.net/7/2193/2014/ doi:10.5194/gmd-7-2193-2014 © Author(s) 2014. CC Attribution 3.0 License. Modeling stomatal conductance in the earth system: linking leaf water-use efficiency and water transport along the soil–plant–atmosphere continuum G. B. Bonan1, M. Williams2, R. A. Fisher1, and K. W. Oleson1 1National Center for Atmospheric Research, P.O. Box 3000, Boulder, Colorado, 80307, USA 2School of GeoSciences, University of Edinburgh, Edinburgh, UK Correspondence to: G. B. Bonan ([email protected]) Received: 2 April 2014 – Published in Geosci. Model Dev. Discuss.: 7 May 2014 Revised: 2 August 2014 – Accepted: 25 August 2014 – Published: 30 September 2014 Abstract. The Ball–Berry stomatal conductance model is model. Similar functional dependence of gs on Ds emerged commonly used in earth system models to simulate biotic from the 1An/1El optimization, but not the 1An/1gs op- regulation of evapotranspiration. However, the dependence timization. Two parameters (stomatal efficiency and root hy- of stomatal conductance (gs) on vapor pressure deficit (Ds) draulic conductivity) minimized errors with the SPA stom- and soil moisture must be empirically parameterized. We atal model. The critical stomatal efficiency for optimization evaluated the Ball–Berry model used in the Community Land (ι) gave results consistent with relationships between maxi- Model version 4.5 (CLM4.5) and an alternative stomatal mum An and gs seen in leaf trait data sets and is related to the conductance model that links leaf gas exchange, plant hy- slope (g1) of the Ball–Berry model. Root hydraulic conduc- ∗ draulic constraints, and the soil–plant–atmosphere contin- tivity (Rr ) was consistent with estimates from literature sur- uum (SPA). The SPA model simulates stomatal conductance veys. The two central concepts embodied in the SPA stomatal numerically by (1) optimizing photosynthetic carbon gain model, that plants account for both water-use efficiency and per unit water loss while (2) constraining stomatal opening for hydraulic safety in regulating stomatal conductance, im- to prevent leaf water potential from dropping below a critical ply a notion of optimal plant strategies and provide testable minimum. We evaluated two optimization algorithms: intrin- model hypotheses, rather than empirical descriptions of plant sic water-use efficiency (1An/1gs, the marginal carbon gain behavior. of stomatal opening) and water-use efficiency (1An/1El, the marginal carbon gain of transpiration water loss). We im- plemented the stomatal models in a multi-layer plant canopy 1 Introduction model to resolve profiles of gas exchange, leaf water poten- tial, and plant hydraulics within the canopy, and evaluated The empirical Ball–Berry stomatal conductance model (Ball the simulations using leaf analyses, eddy covariance fluxes at et al., 1987; Collatz et al., 1991) combined with the Farquhar six forest sites, and parameter sensitivity analyses. The pri- et al. (1980) photosynthesis model was introduced into the mary differences among stomatal models relate to soil mois- land component of climate models in the mid-1990s (Bonan, ture stress and vapor pressure deficit responses. Without soil 1995; Sellers et al., 1996; Cox et al. 1998). The stomatal moisture stress, the performance of the SPA stomatal model conductance model is based on observations showing that was comparable to or slightly better than the CLM Ball– for a given relative humidity (hs), stomatal conductance (gs) Berry model in flux tower simulations, but was significantly scales with the ratio of assimilation (An) to CO2 concentra- better than the CLM Ball–Berry model when there was soil tion (cs), such that gs = g0 + g1hsAn/cs. The model is now moisture stress. Functional dependence of gs on soil mois- commonly used in land surface models for climate simula- ture emerged from water flow along the soil-to-leaf pathway tion. rather than being imposed a priori, as in the CLM Ball–Berry Published by Copernicus Publications on behalf of the European Geosciences Union. 2194 G. B. Bonan et al.: Modeling stomatal conductance in the earth system Part of the scientific debate about the Ball–Berry model of the entire soil-to-leaf path, which is a function of soil prop- has concerned the decline in stomatal conductance to prevent erties, plant hydraulic architecture, xylem construction, and leaf desiccation with high vapor pressure deficit or low soil leaf conductances. Rates of water loss from a leaf cannot, on moisture. The Ball–Berry model uses a fractional humidity at average, exceed the rate of supply without resulting in des- the leaf surface, hs = es/e∗(Tl) = 1 − Ds/e∗(Tl), with es the iccation (Meinzer, 2002). Thus, the collective architecture of vapor pressure at the leaf surface, e∗(Tl) the saturation vapor the soil and plant hydraulic systems controls the maximum pressure at the leaf temperature, and Ds = e∗(Tl)−es the va- rate of water use, and it is widely accepted that there is a por pressure deficit. Leuning (1995) modified the model to limit to the maximum rate of water transport under a given −1 replace hs with (1 + Ds/D0) , where Ds is scaled by the set of hydraulic circumstances. If additional suction beyond empirical parameter D0. Katul et al. (2009) and Medlyn et this point is applied to the continuum, rates of water sup- −1/2 al. (2011b) derived a dependence of gs on Ds based on ply decline, leading to desiccation in the absence of stomatal water-use efficiency optimization. An additional challenge is control (Sperry et al., 1998, 2002). Significant evidence has how to represent stomatal closure as soil moisture declines. accumulated that stomatal conductance and leaf water con- Various empirical functions directly impose diffusive limi- tent are strongly linked to plant and soil hydraulic architec- tations in response to soil drying by decreasing the slope ture (Mencuccini, 2003; Choat et al., 2012; Manzoni et al., parameter (g1) or they impose biochemical limitations and 2013). decrease gs by reducing An as soil water stress increases. Many models of plant hydraulic architecture exist that ex- Neither method completely replicates observed stomatal re- plicitly represent the movement of water to and from the sponses to soil water stress (Egea et al., 2011; De Kauwe leaf (McDowell et al., 2013). Similarly, numerical stomatal et al., 2013), and there is uncertainty about the form of the conductance models have been devised based on principles soil water stress function (Verhoef and Egea, 2014). Some of water-use efficiency optimization and hydraulic safety evidence suggests that both diffusive and biochemical limi- (Friend, 1995; Williams et al., 1996). Despite this, efforts tations must be considered (Zhou et al., 2013). to account for the coupled physics and physiology of wa- An alternative to the Ball–Berry model represents gs di- ter transport along the soil–plant–atmosphere continuum in rectly from optimization theory. This theory assumes that the land surface models used with earth system models have the physiology of stomata has evolved to constrain the rate been limited. of transpiration water loss (El) for a given unit of carbon Here, we adopted (and modified) the stomatal opti- gain (An) (Cowan, 1977; Cowan and Farquhar, 1977). This mization used by the soil–plant–atmosphere model (SPA; optimization can be achieved by assuming that gs varies to Williams et al., 1996, 2001a), which combines both water- maintain water-use efficiency constant over some time pe- use efficiency and a representation of the dynamics of leaf riod (formally this means that ∂An/∂El = constant; note that water potential in the same framework. The SPA model pro- Cowan (1977) and Cowan and Farquhar (1977) discussed op- vides a numerical water-use efficiency optimization within timization in the context of the marginal water cost of carbon the constraints of soil-to-leaf water flow. Stomatal conduc- gain, ∂El/∂An). The empirical Ball–Berry model, despite tance is calculated such that further opening does not yield not being constructed explicitly as an optimality model, is a sufficient carbon gain per unit water loss (defined by the consistent with this theory. Variants of the model can be de- stomatal efficiency parameter ι) or further opening causes rived from the Farquhar et al. (1980) photosynthesis model leaf water potential to decrease below a minimum sustain- based on water-use efficiency optimization, after some sim- able leaf water potential (ψlmin). The model is therefore an plifying assumptions, but the form and complexity of the optimality model with two distinct criteria (water-use effi- stomatal model varies among Rubisco-limited (Katul et al., ciency and hydraulic safety). 2010), light-limited (Medlyn et al., 2011b), or co-limited We compared the stomatal conductance models and tested (Vico et al., 2013) rates. For example, Medlyn et al. (2011b) whether the performance of the alternative models can be −1/2 distinguished in comparisons of model simulations with obtained gs = g0 + 1.6(1 + g1Ds )An/cs when photosyn- thesis is light-limited. However, water-use efficiency opti- eddy covariance flux tower data. First, we tested the Ball– mization does not by itself account for stomatal closure with Berry stomatal conductance model used in the Commu- soil moisture stress. nity Land Model version 4.5 (CLM4.5), the land compo- Additional understanding of stomatal behavior comes nent of the Community Earth System Model. Second, we from the transport of water through the soil–plant– tested the original SPA parameterization, which optimizes in- atmosphere continuum, based on the principle that plants re- trinsic water-use efficiency (iWUE; 1An/1gs, the marginal duce stomatal conductance as needed to regulate transpira- carbon gain of stomatal opening). In that approach, stom- tion and prevent hydraulic failure (Sperry et al., 1998, 2002). atal response to Ds emerges only from stomatal closure Water flows down potential gradients from the soil matrix with low leaf water potential.